A WOLD-LIKE DECOMPOSITION OF TWO-DIMENSIONAL DISCRETE HOMOGENEOUS RANDOM FIELDS
成果类型：
Article
署名作者：
Francos, Joseph M.; Meiri, A. Zvi; Porat, Boaz
署名单位：
Ben-Gurion University of the Negev; Technion Israel Institute of Technology
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004839
发表日期：
1995
页码：
248-260
关键词：
摘要：
Imposing a total order on a regular two-dimensional discrete random field induces an orthogonal decomposition of the random field into two components: a purely indeterministic field and a deterministic field. The deterministic component is further orthogonally decomposed into a half-plane deterministic field and a countable number of mutually orthogonal evanescent fields. Each of the evanescent fields is generated by the column-to-column innovations of the deterministic field with respect to a different nonsymmetrical-half-plane total-ordering definition. The half-plane deterministic field has no innovations, nor column-to-column innovations, with respect to any nonsymmetrical-half-plane total-ordering definition. This decomposition results in a corresponding decomposition of the spectral measure of the regular random field into a countable sum of mutually singular spectral measures.